1. Introduction

Laser-induced breakdown in the bulk of transparent dielectric materials leads to exposure of the material to extreme localized conditions [1, 2]. Laser intensities in excess of 10¹¹ W/cm² are required to achieve intrinsic breakdown in large band gap materials [3]. However, defects in the material can initiate localized breakdown at more than two orders of magnitude lower intensities, as is the case for laser damage caused by nanosecond pulses in practical optical materials. Even though the amount of energy absorbed in the focal volume can be as small as tens of nanojoules, the energy density is high enough that the material can reach localized temperatures in the 1-100 eV range and initial pressures up to 10-1000 GPa followed by the generation of a shockwave [1, 2].

This localized energy deposition is accompanied by a sequence of transient material modifications that lead to the formation of a void. In recent years, dynamical studies of laser-matter interactions using time-resolved imaging have provided valuable insight into complex transient phenomena such as laser-induced shockwave propagation from ablation in a cavity [4] and nanosecond time-scale morphological changes during single laser damage events in transparent solids [5]. However, there is no experimental study that provides information on the transient material modifications as it responds to these extreme conditions throughout the entire timeline of events. Yet, a wide range of material science applications, from laser micro-machining and structural modification of dielectrics to laser-induced damage in high-power laser systems, depend on these fundamental behaviors [1, 2, 6–9]. Furthermore, the physical regime associated with laser-induced modification of materials and sampled by laser damage in dielectrics, i.e. transient and permanent changes occurring in solid density materials after sudden local heating to the 1-10 eV temperature range, is intermediate between that of cold materials and that of high energy density matter encountered in nuclear physics and astrophysics. Both the cold and high energy density physics of material are well studied and modeling tools (such as hydro-codes) exist that have been validated by experiments. However, experimental results that provide an insight into this intermediate range are required to enhance our fundamental understanding and help develop reliable theoretical models.

In this work, we investigate the localized dynamics of material response in bulk fused silica during the cooling phase following localized energy deposition via nanosecond pulse laser-induced breakdown. Specifically, we investigate the material behavior at time delays longer than ~50 ns from the energy deposition when the microscopically visible material modifications (cracks and overall size) have reached their final state. Our experimental approach is two-fold involving time-resolved microscopic imaging of the region of laser energy deposition and pump-and-probe damage testing to isolate the dynamics of the transient absorption. The experimental results suggest that the material response evolves in distinct phases spanning up to about 70 ms from the time of energy deposition.

 

Fig. 1. Experimental layouts depicting (a) time-resolved microscopic imaging system in the trans-illumination (TR) and back-scattering (BS) geometries and (b) non-collinear pump and probe damage testing geometry.

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2. Experimental procedure

The experiments were performed using two independent, nanosecond Q-switched Nd:YAG laser systems (master and slave) that are synchronized using an electronic pulse delay generator. Figure 1(a) illustrates the pump-probe geometry of the time-resolved microscopy system in the trans-illumination (TR) and back-scattering (BS) imaging geometries. A single pulse (pump) at 355-nm from the master laser (~3-ns, full-width at half maximum) was focused in the bulk material to induce intrinsic (deterministic) damage at a fixed irradiance above the damage threshold and prevent surface damage on the 1-cm thick substrates. We estimate that the peak pump irradiance was ~200 GW/cm² based on the measured focal spot radius of ~5 μm in free space (with near Gaussian spatial profile). We note that linear/nonlinear refraction effects are ignored in these calculations; however, the focal spot radius is in good agreement with the transverse dimensions of the damage core region, as discussed below. The slave laser at 532-nm (~4.5-ns) was used to illuminate (at low fluence, without focusing) the damage site and the surrounding volume thus enabling time-resolved imaging of the transient material behavior. The static image spatial resolution was on the order of 1 μm using a lens system consisting of a 5× long-working-distance objective followed by a 5× magnification lens [see Fig. 1(a)]. We note that the dynamic spatial resolution of this microscope system is determined by the speed of the transient events and the pulse duration of the imaging probe pulse. For the time delays investigated in this study, i.e. longer than ~50 ns, the size of the transient and final morphological features of the damage sites is the same, only their contrast is different, therefore the spatial and dynamic image spatial resolution coincide. The images were recorded using a CCD detector with pixel size of 4.4×4.4 μm². The TR geometry in Fig. 1(a) is used to monitor changes in the probe transmission through the damage region due to changes in the material’s complex index of refraction. We note that all images presented in this study have been normalized via pixel-by-pixel division to the pre-damage or final image to factor out any features related to the spatially non-uniform (near gaussian) illumination source and enhance the visibility of transient effects.

Similar to the geometry used in the imaging experiments, the pump-and-probe damage testing experimental setup utilizes a first pulse (pump) to initiate breakdown while a delayed second pulse (probe, also at relatively high fluence) follows in order to test how the final size of a damage site depends on the delay time and energy of the probe pulse. In the system illustrated in Fig. 1(b), the pump and probe beams (at 532-nm, ~3-ns and 355-nm, ~7-ns, respectively) are focused using separate lenses and spatially overlapped in the bulk material. Images of the damage sites in their final state are captured using the same microscope system with illumination provided by a CW helium-neon laser. The pump irradiance was estimated at ~400 GW/cm² (based on the free-space, near Gaussian spatial profile and the focal spot radius of ~5.9 μm), leading to the formation of damage sites on the order of ~100 μm in length, as observed from light-scattering images (corresponding to the cracked region in Fig. 2). The probe peak fluence at 355-nm was varied between 0 and ~80 J/cm² (always small compared to that of the pump at ~1200 J/cm²), with a fixed beam diameter at ~1.5× the size of the damage sites. The overall size of individual sites was quantified in terms of the cross-sectional area of the damage site (i.e., width × height). The material investigated in this study was UV grade fused silica (Sunny Precision Optics) and Corning 7980 glass (CVI Lasers, see [10]) cut to 5 × 5 × 1 cm³ plates with optical quality finish on four sides to allow imaging of damage sites from multiple directions [see Figs. 1(a)–1(b)]. We have not observed any differences in the bulk damage morphology or damage threshold between samples from these two suppliers.

3. Results and discussion

The images shown at the top of Fig. 2 illustrate the images of the transient at 55 ns delay and the final state of the same bulk damage site in fused silica as recorded by our experimental system using the TR geometry. Although only one transient image can be captured from each damage event, the use of intrinsic breakdown initiated by a focused beam enables the study of the entire timeline by capturing images of different, but similarly evolving events. The damage site, as shown in the final image, contains a network of cracks along with an elongated region that is believed to be a filament created by self-focusing. The latter has been modified by the pump pulse and is largely free of cracks. For all images, the pump pulse is propagating as shown by the arrow at the top. Due to the ~32° angle between the direction of propagation of the pump pulse with respect to the image plane not all of the pump-induced modified region can be maintained in focus by the imaging system with a depth of focus of ~50 μm. Therefore, we chose to keep in focus the region of the damage site containing a ’core’ region surrounded by cracks (on the left hand side) while the features on the right hand side of the image are out of focus.

The time-resolved image at 55 ns delay in Fig. 2 (top) indicates that the morphology of the damage site has reached its final stage. However, a closer examination of these images reveals that the image contrast of the main features is different. To better illustrate this effect, we calculated the ratio image via pixel-by-pixel division of the final and transient images. The latter results are shown in Fig. 2 (bottom) for delays between 50 ns and 500 μs indicating a transient reduction in the probe beam transmission through the damaged volume. Specifically, the cracks are visible in the ratio images as bright features arising from lower transmission of the probe beam up to about 300 ns delay. This may suggest the presence of absorption due to transient defects formed on and/or near the crack surface immediately after its formation. Our results indicate that this transient defect population decays within the first 300 ns. The ratio images also show the ’core’ region of the damage site as a bright feature indicating that it may also be associated with a transient absorption for a much longer time, up to about 200 μs delay. We postulate that, in this ’core’ region, the host material properties are in a transient state, i.e. a liquid or vapor phase at high temperatures, giving rise to a transient absorption which has been previously suggested to play a key role during the energy deposition phase [11–13].

The last step in the damage process is the returning of the localized region of the material exposed to high temperatures to solid phase. We hypothesize that this phase change will lead to changes in the scattering properties of the material that may be captured by our imaging system in the backscattering (BS) geometry, as shown in Fig. 1(a). Figures 3(a)–3(b) show the transient (at 60 ms delay) and the corresponding final images, respectively. The image quality is low due to interference effects from scattering of the coherent laser light at multiple scattering sites within the damage site. However, there are subtle differences between the two images which become visible by adjusting the image contrast and are better exposed in the ratio image (transient divided by final) shown in Fig. 3(c). This image reveals an elongated volume of about 7 μm in diameter where the material is still in a transient phase at 60 ms delay time. This effect terminates at about 70 ms, i.e. the damage site reaches its final state.

 

Fig. 2. Typical images of the transient at 55 ns delay and final states of the same damage site induced by the 355-nm pump pulse in the bulk of fused silica (top) and ratio (final divided by transient) images with the same contrast for pump and probe time delays between 50 ns and 500 μs (bottom).

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Fig. 3. Examples of contrast-enhanced (a) transient at 60 ms delay, (b) final and (c) ratio (transient divided by final) images of the same bulk damage site in fused silica.

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The transient features highlighted in the ratio images presented in Figs. 2 and 3 indicate changes in the absorption and/or scattering of the probe laser light incident upon the damaged volume. In order to differentiate between these loss mechanisms, we utilized the pump-and-probe damage testing geometry to indirectly monitor the transient absorption in the damaged region. We postulate that the presence of enhanced absorption by the host material following laser-induced breakdown will lead to higher energy deposition by the probe pulse. This effect in turn will be manifested as a larger in size damage site from the combined exposure to both pump and probe pulses.

The results of pump-and-probe damage testing in fused silica for three different probe fluences as a function of time delay up to 100 μs are summarized in Fig. 4. Typical light-scattering images of bulk damage sites in Fig. 4(a) illustrate the final size of the damage area created by pump only as well as the pump and probe fluence combinations at 100 ns delay. These images have the same color log-scale for better visualization of the pump-induced transient absorption effects. The data points in Fig. 4(b) represent the average damage cross-sectional area measured from the final images at five testing locations for each probe fluence and delay combination. The error bars represent the measurement uncertainty. For comparison, the average damage size due to pump only is also shown by the solid line at constant value corresponding to zero probe fluence. These profiles are directly related to the amount of energy absorbed from the probe pulse and deposited into the material due to the transient material states induced by the pump pulse. For all probe fluences, the profiles exhibit a peak at ~100 ns delay while the transient absorption of the modified material is slowly decaying at 100 μs delay.

 

Fig. 4. (a) Light-scattering images (with the same color log-scale) and (b) the average damage cross-sectional area of typical intrinsic damage sites in bulk fused silica versus pump and probe time delay and fluence.

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The results presented in Fig. 4 suggest the presence of transient optical absorption near the region of laser energy deposition and help the interpretation of the time-resolved images in Figs. 2 and 3. Specifically, the main peak of the transient absorption in the 50–300 ns range of delays observed in Fig. 4(b) can be correlated with the presence of transient absorption manifested in the ratio images of Fig. 2 for the same range of delays, originating in both the crack and ’core’ regions. Figure 2 also suggests that the core region exhibits transient absorption for delays up to about 200 μs which is in agreement with the slow decay of transient absorption observed in Fig. 4(b).

To better support this interpretation, we referred to a recent study of the temporal behavior of the emission during a bulk damage event within optically transparent materials under similar excitation conditions which has demonstrated its blackbody character that reached temperatures on the order of 10⁴ K [1]. For the case of fused silica, the temperature profiles presented in [1] suggest a steady, linear decrease (on a semi-log scale) of the temperature from ~4400 K at 300 ns delay to ~3400 K at 50 μs delay. By extrapolation of this behavior to even longer delay times, we predict temperatures of ~3100 K at 200 μs and ~1900 K at 100 ms, respectively. To understand the relevant temperature range for liquid and vapor phases in fused silica, we note that the temperature for the onset of viscous behavior (glass transition temperature) occurs at about 1310 K while the softening point (defined as the temperature at which the viscosity is 10^7.5 Pa·s) is at 1860 K [10]. To put this into perspective, the temperature at which fused silica flows like honey (at room temperature) is about 2800 K (data from the National Honey Board). As temperature increases, vaporization becomes exponentially more important. Semiconductors have been shown experimentally to suffer band-gap collapse from a combination of electronic screening and structural deformation of the lattice caused by femtosecond laser excitation [14], decaying somewhat slowly after excitation. There are also experimental [15] and theoretical [16] indications of band-gap collapse or narrowing in semiconductors under shock loading. Some degree of band-gap narrowing in dielectrics is to be expected with temperature and this has been shown directly [17] for fused silica at temperatures up to 2000 K and inferred [12] from the measured laser-induced surface damage thresholds of silica which drop rapidly at temperatures above about 2300 K. The transformation of silica to a more absorptive material phase has also been suggested by other measurements performed at much higher temperatures and pressures [18].

 

Fig. 5. SEM image of the axial cross section of a typical bulk damage site in fused silica using ~200 μJ per pulse. The site was ~5 mm from the sample surface with the laser pulse propagating into the page.

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The transient absorption of the ’core’ region at about 200 μs delay drops near the detection limit of the system from the peak value at ~100 ns delay where the attenuation is on the order of 10-20%. The region exhibiting this transient absorption has a diameter of ~10 μm leading to an estimated upper bound value for the peak transient absorption coefficient on the order of 200 cm^-1 (at 532-nm) when the estimated temperature is on the order of 4500 K. In turn, we estimate that for temperatures below ~3100 K the absorption coefficient drops below 20 cm^-1. The time-resolved images in Fig. 3 indicated that the enhanced light scattering from the ‘core’ region (with a diameter of about 7 μm) terminates at 70 ms, suggesting yet another change in the material properties at about ~1900 K. The latter temperature is in excellent agreement with the softening point of fused silica (about 1860 K) [10]. This supports our hypothesis that the melted material returns to solid phase at approximately 70 ms delay from the time of laser energy deposition. In addition, the enhanced scattering from the core region may arise from micro-voids formed by volume contraction during cooling of the material in liquid phase [18, 19].

To correlate the above observations with the microscopic structure of the damage site, the sample was cleaved to expose typical bulk damage sites that were subsequently imaged using scanning electron microscopy (SEM). Figure 5 shows an SEM image of the axial cross section of a damage site indicating the presence of a core region with diameter of ~7 μm. The inner portion of this cylindrical core region of about 3-4 μm in diameter is empty of material (void) while the outer region appears to be homogeneous suggesting that it was formed at a later time as compared to the surrounding, mechanically damaged (cracks, etc.) region. Since the main cause for mechanical damage of the material is the shockwave launched immediately after energy deposition, a logical interpretation of the experimental results is the following: (a) The mechanically damaged region is forming at times shorter than 50 ns. (b) A large population of defects is established in the cracked region and decays within 300 ns. (c) There is a core region that remains in a high temperature, liquid-gas state and exhibits a strong transient absorption for about 200 μs. (d) The material returns to ’solid’ phase at about 70 ms delay.

A reasonable explanation for the observed cooling time is the following. Immediately after laser energy deposition, when temperatures are very high and thermal gradients are very steep, cooling proceeds primarily via heat conduction. Additionally, PdV work and heat of fusion are needed to create and expand the heated region. Radiation cooling is not dominant in the beginning because of the large temperature gradients and not dominant at late times because of the somewhat lower temperatures. Once the heated core region grows to a size of several tens of micrometers, rates of both heat conduction and cooling due to energy spent expanding the core region slow down considerably, allowing a fairly high temperature to persist for times much longer than the laser pulse duration [1]. A theoretical description of this process will be given in a future paper.

4. Conclusion

Our experimental results provide a quantitative description of aspects of the material response, both transient and permanent, following localized energy deposition by a ns scale laser pulse in a dielectric material. In particular, the optical properties of transient material states were probed. The measured material relaxation time was found to be orders of magnitude longer than the laser pulse duration indicating that intrinsic excited material properties were being measured. Our detailed knowledge of such material properties and, therefore, our ability to model material response in this intermediate energy density range, remains limited. An increasing number of related technological applications such as laser machining and laser damage have recently stimulated basic research, including the present work, intended to advance our fundamental understanding in this area. For example, various radiation hydrodynamic codes, validated for modeling material behaviors at higher energy densities, may be suitable for treating the intermediate energy density range probed here. To accomplish this, however, detailed experimental results, such as those presented in this work, are necessary to develop, test and benchmark the physical models of material response used in such codes.